Convergence and stability of randomized implicit two-stage Runge-Kutta schemes
Numerical Analysis
2025-01-17 v3 Numerical Analysis
Abstract
We randomize the implicit two-stage Runge-Kutta scheme in order to improve the rate of convergence (with respect to a deterministic scheme) and stability of the approximate solution (with respect to the solution generated by the explicit scheme). For stability analysis, we use Dahlquist's concept of A-stability, adopted to randomized schemes by considering three notions of stability: asymptotic, mean-square, and in probability. The randomized implicit RK2 scheme proves to be A-stable asymptotically and in probability but not in the mean-square sense.
Cite
@article{arxiv.2404.19059,
title = {Convergence and stability of randomized implicit two-stage Runge-Kutta schemes},
author = {Tomasz Bochacik and Paweł Przybyłowicz},
journal= {arXiv preprint arXiv:2404.19059},
year = {2025}
}